Closed-form control laws for linear time-varying systems

2000 ◽  
Vol 45 (3) ◽  
pp. 537-542 ◽  
Author(s):  
Ping Lu
Keyword(s):  
Closed Form ◽  
Linear Time ◽  
Time Varying ◽  
Control Laws ◽  
Time Varying Systems

scholarly journals A Novel Adaptive Gain of Optimal Sliding Mode Controller for Linear Time-Varying Systems

2019 ◽  
Vol 9 (23) ◽  
pp. 5050 ◽  
Author(s):  
Do Xuan Phu ◽  
Van Mien ◽  
Seung-Bok Choi
Keyword(s):  
Optimal Control ◽  
Sliding Mode ◽  
Linear Time ◽  
Control Law ◽  
Time Varying ◽  
Control Laws ◽  
Control Gain ◽  
Salient Characteristic ◽  
Time Varying Systems ◽  
Main Input

In this study, a new optimal control law associated with the sliding mode control is developed for the linear time-varying system based on the Bolza-Meyer criterion. The salient characteristic of the controller proposed in this work is to have adjustable gains in which the gain values can be larger than 1. This leads to the enhancement of control performances with the given cost function. It is noted here that conventional optimal control laws have a constant gain of 1 or less than 1, and hence, control performances such as the convergence speed are not satisfactory. After formulating the proposed optimal control law for linear time-varying systems, several illustrative examples are adopted and control performances were evaluated to show some benefits of the proposed controller. In particular, three crucial index values of control gain index, main input control index and the state index were investigated. Among illustrative examples, one is related to vibration control problem of the vehicle seat suspension system with magnetorheological (MR) damper. This example is specially treated to evaluate the practical applicability of the proposed optimal controller by considering the measured road profiles; two different random road excitations.

scholarly journals Off-Line Robust Constrained MPC for Linear Time-Varying Systems with Persistent Disturbances

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
P. Bumroongsri ◽  
S. Kheawhom
Keyword(s):  
Linear Time ◽  
Invariant Sets ◽  
Time Varying ◽  
Control Laws ◽  
Output Constraints ◽  
Time Varying Systems ◽  
On Line ◽  
Positively Invariant Set ◽  
Persistent Disturbances ◽  
Positively Invariant Sets

An off-line robust constrained model predictive control (MPC) algorithm for linear time-varying (LTV) systems is developed. A novel feature is the fact that both model uncertainty and bounded additive disturbance are explicitly taken into account in the off-line formulation of MPC. In order to reduce the on-line computational burdens, a sequence of explicit control laws corresponding to a sequence of positively invariant sets is computed off-line. At each sampling time, the smallest positively invariant set containing the measured state is determined and the corresponding control law is implemented in the process. The proposed MPC algorithm can guarantee robust stability while ensuring the satisfaction of input and output constraints. The effectiveness of the proposed MPC algorithm is illustrated by two examples.

scholarly journals The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 99-125
Author(s):  
Edward W. Kamen
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
Linear Time ◽  
Order Term ◽  
Initial Time ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Signals ◽  
Time Varying Systems ◽  
Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

Sign in / Sign up

Export Citation Format

Share Document